Question

A box contains ten sealed envelopes numbered 1. 10. The first three contain no money, the next five each contains $5, and there is a $10 bil in each of the last two. A sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. If X, X, and X, denote the amounts in the selected envelopes, the statistic of interest is the maximum of X, X, and X Obtain the probability distribution of this statistic. (Round your answers to three decimal places.) 10 p(m) 008 X 458 X 533 m

Answer 1

For a randomly selected envelope probability of receiving money is

P(0) = 3/10

P(5) = 5/10

P(10) = 2/10

3 envelopes are selected at random, without replacement

P(0) as maximum = P(0) in 1st *P(0) in 2nd *p(0) in 3rd

= (3/10)^3

= 0.009

P(5 maximum) = P(0)*P(0)*P(5) + P(0)*P(5)*P(0) + P(5)*P(0)*P(0) + P(0)*P(5)*P(5) + P(5)*P(5)*P(0) + P(5)*P(0)*P(5) + P(5)*P(5)*P(5)

= (3/10)^2*(5/10) * 3 + (3/10)*(5/10)^2* 3 + (5/10)^3

= 0.485

P(10 maximum) = 1 - (0.009+ 0.485) = 0.506